By positing a model for optimal brain state transitions, we relate expected energy expenditures to a change in the probability with which a pattern of ECoG power is associated with good memory encoding, directly relating the theory to a desired behavioral feature. This portion of the investigation was made possible by an important modeling advance addressing the challenge of simulating a trajectory whose control is dominated by a single node: the stimulating electrode. This type of control is an intuitive way to model stimulation, where you only want to capture changes resulting from a single input source. However, prior work has demonstrated that while the brain is theoretically controllable from a single point, the amount of energy required can be so large as to make the control strategy impractical [1]}. Here we extend prior models of optimal control [2]}, [3]} by relaxing the input matrix \(\mathbf {B}\)  such that it allows large input to stimulated regions, but also allows small, randomly generated amounts of input at other nodes in the network. Practically, this approach greatly lowers the error of the calculation and also produces narrowly distributed trajectories for the same inputs (see Supplemental Methods).
